1. Field of the Invention
The present invention relates to a lens system, and more particularly, to a lens system which is applied to an optical beam scanner, such as a laser printer, which scans a plurality of optical beams on a recording surface.
2. Description of the Prior Art
Japanese Patent Laying-Open Gazettes Nos. 195211/1984 and 267910/1988 disclose lens systems which can be applied to an optical beam scanner such as a laser printer, respectively.
FIG. 1 illustrates the structure of a conventional telecentric f-.theta. lens system, which is disclosed in the former gazette Japanese Patent Laying-Open Gazette No. 195211/1984). As shown in FIG. 1, the conventional telecentric f-.theta. lens system is formed with a negative meniscus lens L.sub.12 whose concave surface S.sub.12 is directed toward an entrance pupil EP, positive meniscus lenses L.sub.13 and L.sub.14 and a positive plano-convex lens L.sub.15, and these lenses L.sub.12 to L.sub.15 are arranged in order from the entrance pupil EP side toward a recording surface RS side.
The aforementioned lens system satisfies: EQU h=f.multidot..theta.
assuming that h represents a distance from an optical axis Z of the lens system to a beam spot on the recording surface RS, f represents the focal length of the lens system and .theta. represents an incident angle of the beam upon the lens system. A laser beam is generally deflected by a polygon mirror, so that the laser beam is impinged on the recording surface RS through the lens system. Since the polygon mirror is rotated at a constant angular velocity, the beam spot moves on the recording surface RS at a constant speed.
Further, the lens system has a telecentric characteristic that all principal rays substantially vertically enter the recording surface RS, so that an image size in a main scanning direction does not vary even if the recording surface RS is displaced in the direction of the optical axis Z, for example, as is well known in the art.
Therefore, a telecentric f-.theta. lens system is employed in a laser printer etc. particularly requiring that a laser beam is projected onto the recording surface in high accuracy.
FIG. 2 shows a schematic illustration of the optical path deflected by a deflector 1. A plurality of laser beams B.sub.0 to B.sub.n are projected onto a point O of the deflector 1 which rotates in the forward and reverse directions around a Y-axis, while laser beams b.sub.0 to b.sub.n deflected by the deflector 1 are directed toward a recording surface RS (X-Y plane) through a lens system 2a. In the figure, symbols i.sub.0 to i.sub.n represent beam spots of the laser beams b.sub.0 to b.sub. on the recording surface RS, respectively.
In the case that an f-.theta. lens system shown in FIG. 1 is employed as the lens system 2a, the following equation is obtained: ##EQU1##
Where y is a distance between the beam spots i.sub.0 and i.sub.n, f is a focal length of the f-.theta. lens system 2a, .alpha. is an angle between the laser beam B.sub.n and an optical axis X, and .beta. is an angle between the laser beam b.sub.0 and an optical axis Z of the f-.theta. lens system 2a.
When the deflector 1 rotates around the Y-axis, the angle .beta. varies corresponding to the rotation of the deflector 1, whereby the distance y varies with the angle .beta.. Therefore, the locus of the laser beams focusing on the recording surface RS by the f-.theta. lens system 2a will not straight as shown in FIG. 3, so that the quality of an image recording on the recording surface RS is lowered.
FIG. 4 illustrates the structure of an f-sin.theta. lens system, which is disclosed in latter gazette (Japanese Patent Laying-Open Gazette No. 267910/1988). As shown in FIG. 4, the f-sin.theta. lens system is formed with a first lens group G.sub.1 having a negative focal length and a second lens group G.sub.2 having a positive focal length, to satisfy: EQU h=f.multidot.sin.theta.
where h is a distance between an optical axis Z of the f-sin.theta. lens system and a beam spot b on a recording surface RS, f is a focal length of the f-sin.theta. lens system and .theta. is an incident angle that the optical beam entering the lens system forms with respect to the optical axis Z thereof.
In the case that the f-sin.theta. lens system 2 is used instead of the lens system 2a as shown in FIG. 2, the following equation is obtained: EQU y=f.multidot.sin.alpha.
As understood the above equation, the distance y is a constant even if the deflector 1 rotates in the forward and reverse direction around the Y-axis. Therefore, the loci of the plural laser beams will be straight as shown in FIG. 5, when the laser beams are directed to the recording surface RS through the f-sin.theta. lens system.
However, the f-sin.theta. lens system shown in FIG. 5 has no telecentric characteristic, so that an image size in a main scanning direction varies with the displacement of the recording surface RS in the direction of the optical axis Z of the f-sin.theta. lens system. Therefore, the lens system can't be employed in the optical beam scanner such as a laser printer requiring that the image can be recorded on the recording surface RS in high accuracy.